Continuity
This lesson on continuity covers the definition of continuity at a point, left and right continuity, and continuity on an interval for polynomials, rational functions, and trigonometric functions. The lesson also covers different types of discontinuities, such as jump, infinite, and removable discontinuities. The properties of continuous functions are also discussed, along with compositions of functions and one-sided continuity. The intermediate value theorem and its corollary for finding zeros of functions are briefly mentioned as consequences of continuity.
Definition of continuity at a point. Continuity of polynomials, rational functions, and trigonometric functions. Left and right continuity. Continuity on an interval.
Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.
- Continuity at a point - Practice finding continuity at a point.
- Continuity on an Interval - Practice finding continuity on an interval.
- One-Sided Continuity - Practice finding one-sided continuity.
- The intermediate value theorem - Practice with the Intermediate Value Theorem.
- Boundedness; The Extreme Value Theorem - Practice with boundedness and the Extreme Value Theorem.
- What is the definition of continuity?
- When is a function continuous?
- What is a discontinuity?
- What is a jump discontinuity?
- What is an infinite discontinuity?
- What is a vertical asymptote?
- What is a removable discontinuity?
- When are polynomials continuous?
- When are rational functions continuous?
- When are sin and cos continuous?
- What are the rules of limits of compositions?
- What is one-sided continuity?
- What is the Intermediate Value Theorem?
- What is the Extreme Value Theorem?
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Staff Review
This video does a great job of explaining clearly and plainly what it means for a function and a graph to be continuous. Again, several examples are stepped through and explained. Discontinuities are explained and defined as well. Many important theorems and corollaries are explained. A very complete lesson.
